Daniel travelled north for 19 miles and then east for 13 miles. Determine, to the nearest tenth of a mile, how far he is from his starting point.
North and south run vertical: up and down. North, you go up; south, you go down. East and west run horizontal. West, you go to the left; east, you go to the right. And these lines are perpendicular, which means they make 90-degree angles. First, Daniel travelled 19 miles north. From there, he travelled 13 miles east. How far is he from where he started?
So we wanna know the distance between these points; we will call it 𝑥. It’s important to know that there is a 90-degree angle involved. Since we travel north and then east, those lines are perpendicular, which means there’s a 90-degree angle. So this is a right triangle. So we can use the Pythagorean theorem whereas the sum of the squares of the shorter sides is equal to the square of the longest side. And that longest side is the one across from the 90-degree angle, called the hypotenuse.
So we have 19 squared plus 13 squared equals 𝑥 squared. 19 squared is 361; 13 squared is 169. And then we bring down our 𝑥 squared. 361 plus 169 is 530. And now we need to isolate 𝑥; we need to get 𝑥 by itself. 𝑥 is being squared. And the inverse operation of squaring something is to square root it, so let’s go ahead and square root both sides of the equation.
The square root of 530 is 23.02; however, it says to round to the nearest tenth of a mile. So we need to round one decimal place. So we need to decide if the zero will stay a zero or round up to one. So we’ll look at the two to the right of it. Since two is less than five, zero will stay at zero. This means Daniel is 23.0 miles from his starting point.